User`s guide

Smoothing Data
2-9
Smoothing Data
If your data is noisy, you might need to apply a smoothing algorithm to expose
its features, and to provide a reasonable starting approach for parametric
fitting. The two basic assumptions that underlie smoothing are
• The relationship between the response data and the predictor data is
smooth.
• The smoothing process results in a smoothed value that is a better estimate
of the original value because the noise has been reduced.
The smoothing process attempts to estimate the average of the distribution
of each response value. The estimation is based on a specified number of
neighboring response values.
You can think of smoothing as a local fit because a new response value is
created for each original response value. Therefore, smoothing is similar to
some of the nonparametric fit types supported by the toolbox, such as
smoothing spline and cubic interpolation. However, this type of fitting is not
the same as parametric fitting, which results in a global parameterization of
the data.
Note You should not fit data with a parametric model after smoothing,
because the act of smoothing invalidates the assumption that the errors are
normally distributed. Instead, you should consider smoothing to be a data
exploration technique.
There are two common types of smoothing methods: filtering (averaging) and
local regression. Each smoothing method requires a span. The span defines a
window of neighboring points to include in the smoothing calculation for each
data point. This window moves across the data set as the smoothed response
value is calculated for each predictor value. A large span increases the
smoothness but decreases the resolution of the smoothed data set, while a
small span decreases the smoothness but increases the resolution of the
smoothed data set. The optimal span value depends on your data set and the
smoothing method, and usually requires some experimentation to find.